A square is a rhombus but a rhombus is not a square
This sentence is not accurate as a square is a rhombus but need not say a rhombus need not be a square. A rhombus is only 1 type of square like how a square is only 1 type of a parallelogram.The rhombus, like the square both have equal lengths fro 1 side, both are parallel to its opposite side, but a square has a right angle on every side, but the rhombus need not have right angles on every side so a rhombus can be a tinted square.
No, a parallelogram can be a square but a square need not be a parallelogram as parallelograms and squares are both figures with opposite sides that are parallel , however, the square has all equal sides and is also right angled on very side which can be a parallelogram, but it may not be as a square is only 1 type of parallelogram.
Q5- Yes as if ABCD is a parallelogram, AD and BC, AB and CD are parallel. So if F and E are in the middle, and B and D are at the meeting points of the sides, then both FD and BE are parallel, so it is a parallelogram as BF is also equal to ED as they land on the same line as AD and BC.